Markowitz Model

The research on the Markowitz model and optimization of its portfolio using a variety of evaluation indicators and meta-beta-algorithms has always been the focus of attention of accounting and finance researchers. The results of studies carried out by various types of optimization methods are different in the Markowitz modified models. The purpose of this study is to measure the optimal portfolio and its corresponding return, with respect to the portfolio in the traditional Markowitz model, as well as to compare the position of the refining and petrochemical companies versus stock market outperformers, through integrating the operational criteria and the new indicators of liquidity using the genetic algorithm in the Markowitz model. Therefore, financial data related to the research variables for 35 cases of TSE-listed refinery and petrochemical companies from 2012 to 2016 fiscal years were extracted from Rahavard Novin database software and simulated by the genetic algorithm. The results show that returns on the stock portfolio optimized using the genetic algorithm and without considering the liquidity limitations and filters have a significant and positive difference with the return on the stock portfolios optimized with regard to the liquidity limitations and filters. Furthermore, the application of liquidity limitations and filters in the formation of optimal stock portfolios leads to a conservative increase in the choice of stocks (portfolio formation), which leads to a reduction in the risk and return of investment in such portfolios.

Portfolio optimization which means choosing the right stocks based on the highest return and lowest risk, is one of the most effective steps in making optimal investment decisions. Deciding which stock is in a better position compared to other stocks and deserves to be selected and placed in one's investment portfolio and how to allocate capital between these stocks, are complex issues. Theoretically, the issue of choosing a portfolio in the case of minimizing risk in the case of fixed returns can be solved by using mathematical formulas and through a quadratic equation; but in practice and in the real world, due to the large number of choices in capital markets, the mathematical approach used to solve this model, requires extensive calculations and planning. Considering that the behavior of the stock market does not follow a linear pattern, the common linear methods cannot be used and useful in describing this behavior. In this research, portfolio optimization using the gray wolf algorithm and the Markowitz model based on CO-GARCH modeling has been investigated. The statistical population of the current research included the information of 698 companies from the companies admitted to the Tehran Stock Exchange for the period of 2011 to 2020. First, the optimal investment model is presented based on the gray wolf algorithm, and After extracting the optimal model, the efficiency of the gray wolf algorithm is compared with the Markowitz model based on CO-GARCH modeling.